Question: Rewrite as a simplified fraction. ${0.58\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 586.6666...\\ 100x &= 58.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 528}$ ${x = \dfrac{528}{900}} $ ${x = \dfrac{44}{75}} $